## Analysis of Home Prices and Market Returns### Home Price Survey in a Metropolitan AreaA study of 40 home prices in a metropolitan area yielded the following results:| Price | Less than $200,000 | Equal to $200,000 | More than $200,000 ||---------------------|--------------------|-------------------|--------------------|| Number of homes | 13 | 1 | 27 |### Hypothesis Testing1. **Hypothesis 1:** - Test if the median price in the metropolitan area is $200,000.2. **Hypothesis 2:** - Test if the median price in the metropolitan area is more than $200,000.Both tests use a significance level of α = 0.05. Formulate your hypotheses, apply the binomial approach, and detail your calculations, including p-values for both hypotheses.### Regression Analysis on Market ReturnsA proposed relationship between annual security return and market return can be defined by the regression model:\[ y = mx + b + \varepsilon \]- **y**: Annual return of the security- **x**: Annual return of the market- **b**: Intercept- **ε**: Normally distributed noise**Return** is calculated as:\[ \text{Return} = \text{value at end of the year} + \text{received dividends during the year} - \text{value at the beginning of the year} \]### Model Testing Approach1. Retrieve annual data for a security of your choice and a financial index like the S&P 500 as the market indicator.2. Use the past 20 years as your timeframe for analysis.3. Conduct a regression analysis that includes hypothesis testing.4. Report findings, include conclusions, significance levels, and present the final regression model.5. Provide a scatterplot with the regression line, analyze residuals, and check their normality.Consider if the model is valid. Determine whether there is a positive or adverse influence and specify if your regression model shows outperformance or underperformance relative to the market. Provide a detailed explanation of your work.

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4. A survey of 40 home prices in a metropolitan area has the following results. Price Less than $200,000 Equal to $200,000 More than $200,000 Number of homes 13 1 27 1. Test the hypothesis that the median price in the metropolitan is $200,000 2. Test the hypothesis that the median price in the metropolitan is more than $200,000 a = 0.05 in both cases. Include hypothesis formulation, use the binomial approach, and explain your calculations in detail. Include p values in both cases.

4. A survey of 40 home prices in a metropolitan area has the following results. Price Less than $200,000 Equal to $200,000 More than $200,000 Number of homes 13 1 27 1. Test the hypothesis that the median price in the metropolitan is $200,000 2. Test the hypothesis that the median price in the metropolitan is more than $200,000 a = 0.05 in both cases. Include hypothesis formulation, use the binomial approach, and explain your calculations in detail. Include p values in both cases.

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Concept explainers

2-Proportion Test

In a 2-proportion test, two separate proportions are measured at the same time, and their similarity is evaluated. It is also known as a 2-proportion z-test, and a comparison of two different proportions is done in this method.

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Question

## Analysis of Home Prices and Market Returns

### Home Price Survey in a Metropolitan Area

A study of 40 home prices in a metropolitan area yielded the following results:

| Price | Less than $200,000 | Equal to $200,000 | More than $200,000 |
|---------------------|--------------------|-------------------|--------------------|
| Number of homes | 13 | 1 | 27 |

### Hypothesis Testing

1. **Hypothesis 1:**
- Test if the median price in the metropolitan area is $200,000.

2. **Hypothesis 2:**
- Test if the median price in the metropolitan area is more than $200,000.

Both tests use a significance level of α = 0.05. Formulate your hypotheses, apply the binomial approach, and detail your calculations, including p-values for both hypotheses.

### Regression Analysis on Market Returns

A proposed relationship between annual security return and market return can be defined by the regression model:

\[ y = mx + b + \varepsilon \]

- **y**: Annual return of the security
- **x**: Annual return of the market
- **b**: Intercept
- **ε**: Normally distributed noise

**Return** is calculated as:
\[ \text{Return} = \text{value at end of the year} + \text{received dividends during the year} - \text{value at the beginning of the year} \]

### Model Testing Approach

1. Retrieve annual data for a security of your choice and a financial index like the S&P 500 as the market indicator.
2. Use the past 20 years as your timeframe for analysis.
3. Conduct a regression analysis that includes hypothesis testing.
4. Report findings, include conclusions, significance levels, and present the final regression model.
5. Provide a scatterplot with the regression line, analyze residuals, and check their normality.

Consider if the model is valid. Determine whether there is a positive or adverse influence and specify if your regression model shows outperformance or underperformance relative to the market. Provide a detailed explanation of your work.

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